Switched Beam Antennas support radio positioning via Angle Of Arrival (AOA) information collected from nearby devices. Using an analytical approach, first we present the Cramér–Rao Bound (CRB) for AOA estimates using identically and equally spaced antenna elements. Then we analyze the results to devise design guidelines for improved AOA estimation. The design parameters considered are: 1) the number of antenna elements, 2) their directivity, and 3) the type of polarization. The effect of each parameter is discussed in detail; additionally, experimental results at 2.45 GHz are reported to evaluate the effect of different antenna polarization on the CRB.